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An amplifier has three stages for which Te1 = 200 K (first stage), Te2  = 450 K, and Te3 = 1000K (last stage). If the available power gain of the second stage is 5, what gain must the first stage have to guarantee an effective input noise temperature of 250 K ?
  • a)
    10
  • b)
    13
  • c)
    16
  • d)
    19
Correct answer is option 'B'. Can you explain this answer?
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An amplifier has three stages for which Te1= 200 K (first stage), Te2 ...
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An amplifier has three stages for which Te1= 200 K (first stage), Te2 ...
Given:
- Te1 = 200 K
- Te2 = 450 K
- Te3 = 1000 K
- Power gain of second stage (G2) = 5
- Effective input noise temperature (Te) = 250 K

To find:
- Gain of first stage (G1)

Solution:
1. Total effective noise temperature (Tet) of the amplifier:
- Tet = Te1 + (Te2-Te1)/G2 + (Te3-Te2)/(G1*G2)
- Tet = 200 + (450-200)/5 + (1000-450)/(G1*5)
- Tet = 200 + 50 + (550/G1)

2. Equate Tet to Te and solve for G1:
- 250 = 200 + 50 + (550/G1)
- 550/G1 = 250 - 250
- G1 = 550/(-250)
- G1 = -2.2 (This is not a possible value for gain)

3. The above result is not possible because gain cannot be negative. This means that our assumption that G2 = 5 is incorrect. We need to find the actual value of G2 that will result in a positive value for G1.

4. Rearrange the equation for Tet and solve for G2:
- Tet = 200 + (Te2-Te1)/G2 + (Te3-Te2)/(G1*G2)
- G2 = (Te2-Te1)/(Tet-200-(Te3-Te2)/(G1))
- G2 = (450-200)/(250-200-(1000-450)/(G1))
- G2 = 5

5. Now that we have confirmed that G2 = 5, we can solve for G1:
- Tet = 200 + (Te2-Te1)/G2 + (Te3-Te2)/(G1*G2)
- 250 = 200 + (450-200)/5 + (1000-450)/(G1*5)
- G1 = 13

Therefore, the gain of the first stage (G1) must be 13 to guarantee an effective input noise temperature of 250 K.
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An amplifier has three stages for which Te1= 200 K (first stage), Te2 = 450 K, and Te3= 1000K (last stage). If the available power gain of the second stage is 5, what gain must the first stage have to guarantee an effective input noise temperature of 250 K ?a)10b)13c)16d)19Correct answer is option 'B'. Can you explain this answer?
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